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Two-Phase Wave Interactions and Peri...

Mao, Yifeng.

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Two-Phase Wave Interactions and Periodic Wavemaker Problem in Dispersive Hydrodynamics.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Two-Phase Wave Interactions and Periodic Wavemaker Problem in Dispersive Hydrodynamics./
作者:	Mao, Yifeng.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2023,
面頁冊數:	218 p.
附註:	Source: Dissertations Abstracts International, Volume: 85-06, Section: B.
Contained By:	Dissertations Abstracts International85-06B.
標題:	Applied mathematics. -
電子資源:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30811749
ISBN:	9798381165340

Two-Phase Wave Interactions and Periodic Wavemaker Problem in Dispersive Hydrodynamics.
Mao, Yifeng.

Two-Phase Wave Interactions and Periodic Wavemaker Problem in Dispersive Hydrodynamics. - Ann Arbor : ProQuest Dissertations & Theses, 2023 - 218 p.

Source: Dissertations Abstracts International, Volume: 85-06, Section: B.

Thesis (Ph.D.)--University of Colorado at Boulder, 2023.

This item must not be sold to any third party vendors.

Waves and their interactions are ubiquitous in nature. While linear wave equations exhibit a superposition principle, nonlinear wave equations generally do not. Previous research has delved into the mathematics of solitary waves (solitons), dispersive shock waves, and their interactions within the field of dispersive hydrodynamics. However, a more complicated class of problems, including periodic traveling waves and their interactions across multiple phases, presents a rich and physically meaningful area that motivates further investigation. Inspired by this, the primary objective of this thesis is the mathematical and experimental study of nonlinear wave interactions, starting from the generation and propagation of one-phase periodic traveling waves and extending to their two-phase interactions with solitons and with one another.The thesis focuses on multiscale nonlinear wave phenomena within a dispersive hydrodynamic framework in which waves in fluid and fluid-like systems are subject to dispersion that dominates dissipation. The research combines analytical and asymptotic techniques, numerical simulations, and experimental observations. Of particular interest in the thesis are the linear and nonlinear wave dynamics in two specific equations: the Korteweg-De Vries (KdV) equation and the conduit equation. The KdV equation is a well-known model for weakly nonlinear surface waves in shallow water. Meanwhile, the conduit equation serves as a model for nonlinear interfacial wave dynamics in a viscous two-fluid core-annular flow, where a pressure-driven core fluid is within an annulus of another miscible, heavier fluid with a small viscosity ratio between the two. The study begins with one-phase periodic traveling waves by deriving the exact dispersion relation for linear interfacial waves in the two-fluid Stokes equations and comparing them with experiments. The radiation condition for the wavemaker problem in physics that selects the unique outgoing wave is mathematically proved using a new asymptotic approach. Nonlinear periodic traveling waves in the core-annular flow system are experimentally characterized. Subsequently, experimental and theoretical investigation of nonlinear interactions between solitons and periodic traveling waves is undertaken, resulting in the emergence of traveling breathers. Special cases involving two-phase periodic wave interactions are theoretically described using an asymptotic approach called Whitham modulation theory.

ISBN: 9798381165340Subjects--Topical Terms:

2122814
Applied mathematics.
Subjects--Index Terms:

Dispersive hydrodynamics

Two-Phase Wave Interactions and Periodic Wavemaker Problem in Dispersive Hydrodynamics.
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520 $a Waves and their interactions are ubiquitous in nature. While linear wave equations exhibit a superposition principle, nonlinear wave equations generally do not. Previous research has delved into the mathematics of solitary waves (solitons), dispersive shock waves, and their interactions within the field of dispersive hydrodynamics. However, a more complicated class of problems, including periodic traveling waves and their interactions across multiple phases, presents a rich and physically meaningful area that motivates further investigation. Inspired by this, the primary objective of this thesis is the mathematical and experimental study of nonlinear wave interactions, starting from the generation and propagation of one-phase periodic traveling waves and extending to their two-phase interactions with solitons and with one another.The thesis focuses on multiscale nonlinear wave phenomena within a dispersive hydrodynamic framework in which waves in fluid and fluid-like systems are subject to dispersion that dominates dissipation. The research combines analytical and asymptotic techniques, numerical simulations, and experimental observations. Of particular interest in the thesis are the linear and nonlinear wave dynamics in two specific equations: the Korteweg-De Vries (KdV) equation and the conduit equation. The KdV equation is a well-known model for weakly nonlinear surface waves in shallow water. Meanwhile, the conduit equation serves as a model for nonlinear interfacial wave dynamics in a viscous two-fluid core-annular flow, where a pressure-driven core fluid is within an annulus of another miscible, heavier fluid with a small viscosity ratio between the two. The study begins with one-phase periodic traveling waves by deriving the exact dispersion relation for linear interfacial waves in the two-fluid Stokes equations and comparing them with experiments. The radiation condition for the wavemaker problem in physics that selects the unique outgoing wave is mathematically proved using a new asymptotic approach. Nonlinear periodic traveling waves in the core-annular flow system are experimentally characterized. Subsequently, experimental and theoretical investigation of nonlinear interactions between solitons and periodic traveling waves is undertaken, resulting in the emergence of traveling breathers. Special cases involving two-phase periodic wave interactions are theoretically described using an asymptotic approach called Whitham modulation theory.
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